How to orbit with finer precision
You can change Orbit Sensitivity in the Preferences(F4 -> p): 



You could also add two entries to your keymap to make a key that you could press and while it's pressed the sensitivity is set to some value, but when you release it, it resets it to some other: 



Note that one is set to "Press", another to "Release".
The operator: wm.context_set_value sets the value for preferences.inputs.view_rotate_sensitivity_turntable here. You would have to play with the values to find the ones comfortable for you(mine are quite low, because I am using a pen tablet right now). 

It doesn't work while you are orbiting, you have to press and hold the key before you start. It might be possible to make it work while you orbit, but that would require a more complex approach.